Answers
Answer:
123
Step-by-step explanation:
Squaring the given equation gives
[tex]t^2+(2\cdot t \cdot \frac{1}{t} )+ \frac{1}{t^2}=9.[/tex]
The [tex]t[/tex] and [tex]\frac{1}{t}[/tex] terms cancel out nicely, which is one of the reasons for squaring the equation.
Simplifying gives
[tex]t^2+2+\frac{1}{t^2}=9,[/tex]
[tex]t^2+\frac{1}{t^2}=7.[/tex]
The question asks for [tex]t^5+\frac{1}{t^5},[/tex] so we can square the equation again and simplify to get higher powers into the expression:
[tex](t^2+\frac{1}{t^2})^2=49,[/tex]
[tex]t^4+(2 \cdot t^2 \cdot \frac{1}{t^2}) + \frac{1}{t^4}=49,[/tex]
[tex]t^4+2+ \frac{1}{t^4}=49,[/tex]
[tex]t^4+\frac{1}{t^4}=47.[/tex]
Multiplying this expression by [tex]t+\frac{1}{t}[/tex] to try and get a fifth power gives
[tex](t^4+\frac{1}{t^4})(t+\frac{1}{t})=t^5+t^3+\frac{1}{t^3}+\frac{1}{t^5}.[/tex]
The only thing left we need is [tex]t^3+\frac{1}{t^3}[/tex] to subtract from this; we know everything else. Since [tex]t^3+\frac{1}{t^3}[/tex] can be written as [tex](t+\frac{1}{t})(t^2-1+\frac{1}{t^2}),[/tex] we can simply plug in the values we know for [tex]t+\frac{1}{t}[/tex] and [tex]t^2+\frac{1}{t^2}:[/tex]
[tex]t^3+\frac{1}{t^3}=(3)(7-1)=18.[/tex]
All that is left is to plug it in our equation here:
[tex](t^4+\frac{1}{t^4})(t+\frac{1}{t})=t^5+t^3+\frac{1}{t^3}+\frac{1}{t^5},[/tex]
[tex](47)(3)=t^5+\frac{1}{t^5}+18,[/tex]
Multiplying and rearranging gives:
[tex]t^5+\frac{1}{t^5}=123.[/tex]
Related Questions
A company is selecting 6 people to be on a committee. There are 26 employees eligible to be on the committee. What is the total number of ways the committee may be formed if the employees are selected at random and each employee will have a different position on the committee
Answers
C(26, 6) = 230,230 possible sets....!!
Need this tonight, no joking around, circled B as a placeholder, tell me the right one
Answers
PLS HELP HURRY !!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
no solution
Step-by-step explanation:
-2y-3y+8=8-5y-12
-2-3y=-5y
-5y+8=8-5y-12
inverse operation: add 5y to both side
-5y+8=8-5y-12
+5y +5y
-5y+5y=0, so it cancels out both -5ys
8=8-12
8=-4
there is no value for y to make the equation true, so there is no solution
¿Alguien sabe como se llaman estas figuras en inglés?
Answers
Answer:
7. parallelogram
8. square
9. trapezoid (trapezium) (maybe "acute" - can't see the whole image)
10. rhombus
11. ?
12. rectangle
13. equilateral triangle
14. scalene triangle
15, 16, 17 and 18 are all isosceles triangles as they have 2 sides of equal length
What’s a number between 10 and 11?
I NEED HELP. DON’T TROLL
Answers
Answer:
You start with the decimals place since you can't go any further than another whole number.
10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9 and so on, in the tenths hundredths and thousandths place.
There can be only rational numbers or decimals
For example
10.210.710.310.23310.89I need more brainliest I will answer your questions if need. 25 points
Answers
Answer:
Why is the energy that results from a roller coaster's position at the top of a hill referred to as potential energy?
Step-by-step explanation:
.
Answer
if x=3 find y
y- x^3+x^2+9
Step-by-step explanation:
ASAP PLSSS ALL MY POINTS Use sigma notation to represent the sum of the first seven terms of the following sequence: 4, 10, 16, …
the summation from n equals 1 to 7 of negative 4 plus 6 times n
the summation from n equals 1 to 7 of 4 plus 6 times n
the summation from n equals 1 to 7 of 2 plus 6 times n
the summation from n equals 1 to 7 of negative 2 plus 6 times n
Answers
Answer:
Step-by-step explanation:
Answer:
i really need help on this one too
Step-by-step explanation:
.
Which best describes the range of the function f(x) = 2/3(6)^xafter it has been reflected over the x-axis?
Answers
which image is a translation
Answers
Answer:
The second one
can somone help me with tjis pls
Answers
Answer:
LinePlanePlease mark as Brainliest
By using the definition of collinear and coplanar points, we will see that
7) Collinear points: All lie on the same line.8) Coplanar points: All lie on the same plane.What do collinear and coplanar mean?We say that a given set of points is collinear if all the points belong to the same line, just to give an example, any pair of two points is collinear, as we always can find a line that passes through two points.
On other hand, a set of points is coplanar if the points lie on the same plane. Remember that a plane is defined by a line and a point outside of it.
With these definitions in mind, we can answer:
7) Collinear points: All lie on the same line.8) Coplanar points: All lie on the same plane.If you want to learn more about collinear and coplanar, you can read:
https://brainly.com/question/1593959
solve system of equations:
4x + 3y = 10
3x + y = 15
Answers
Answer:
x= 7 y= -6
Step-by-step explanation:
brainliest plzzz
how do you calculate the LCM for 128 and 256
Answers
Answer:
I think its 256
Step-by-step explanation:
The LCM of 128 and 256 is 256. Steps to find LCM. Find the prime factorization of 128 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2; Find the prime factorization of 256.
Answer:
256
Step-by-step explanation:
1- Find the prime factorization of 128
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
2- Find the prime factorization of 256
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
3- Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
4- LCM = 256
A die is rolled 3 times. What is the
probability of getting I's on each
roll?
Answers
Answer:
1/6 I think. but for each individual its 1/6 but for all three, i don't know sorry
Step-by-step explanation:
Which situation is best represented by the equation below? m = 7h + 4 Fran makes and sells hats. The selling price for each of her last 7 hats was $4. What is m, the amount of money Fran made Bobby has 7 times as many cowboy hats in his collection as Norm. Norm has 4 more fishing hats in his collection than BobE Cara earns $7 per hour babysitting plus $4 for transportation. What m, the amount of money Cara makes for h hours of b. Seven people contributed to a fundraiser and raised 4 times as much money as was needed, h. How much money, m, did the
Answers
Answer:
Cara earns $7 per hour babysitting plus $4 for transportation.
Step-by-step explanation:
When Cara works for 1 hour, she earns 7*1 + 4 = 11 dollars. The value of h increments as Cara babysits longer, but she gains the 4 dollar transportation fee regardless of her workhour.
What is the equation of the line that passes through the point (3,−3) and has a slope of 0?
Answers
Answer:
x = 3
Step-by-step explanation:
A line with a slope of 0 is a horizontal line parallel to the x- axis with equation
x = c
where c is the value of the x- coordinates the line passes through.
the line passes through (3, - 3 ) with x- coordinate 3 , then
x = 3 ← equation of line
Answer:
f(x) = -3
Step-by-step explanation:
it will be a constant function because if the slope = 0, the y value is not changing
so the equation of the line, f(x) = ax+b, will be f(x) = 0x+b
f(x) = b, b is the y value here
9+16x=17x+4 solve for x
Answers
[tex]9 + 16x = 17x + 4 \\ 9 - 4 = 17x - 16x \\ 5 = x[/tex]
hope this helps!
~god bless you~
~diva~
Need the answer super confusing for me
Answers
Answer:
A) True
B) False
C) True
Step-by-step explanation:
Can u answer 25 1/3 - 17 5/6
Answers
Answer:
[tex] \boxed{ \sf{7 \frac{1}{2} }}[/tex]
Step-by-step explanation:
convert to fraction form a/b
25 1/3 - 17 5/6
[tex]25 \frac{1}{3} = \frac{25 \times 3 + 1}{3} = \frac{76}{3} [/tex]
[tex]17 \frac{5}{6} = \frac{17 \times 6 + 5}{6} = \frac{107}{6} [/tex]
Now, we have 76/3 - 107/6
→ Solution[tex] \frac{76}{3} - \frac{107}{6} [/tex]
[tex] \frac{76 \times 2}{6} - \frac{107}{6} [/tex]
[tex] \frac{152}{6 } - \frac{107}{6} [/tex]
[tex] \frac{45}{6} [/tex]
simplify
[tex] \purple{ \boxed{ \frac{45}{6} = 7 \frac{3}{6} = 7 \frac{1}{2} }}[/tex]
1.38 × 14 long multiplication
Answers
Explanation:
1.38•14
______
19.32
21. In 2019, the population in Modesto is 212,616. The annual growth rate of Modesto is 2%. Write an
exponential model to represent the population of Modesto. Then use this model to estimate the population after 8 years.
Answers
Answer:
A general formula for calculating the population growth rate is Gr = N / t. Gr is the growth rate measured in individuals, N is the change in population, and t is the period of time.
Step-by-step explanation:
SM
2. Given g(x) =1/2x+5, find the following.
a. g(4)
b. g(-10)
C. g(0)
Can someone please help me?
Answers
Answer:
Look below
Step-by-step explanation:
To do this, we have to substitute each number for x...
a. [tex]g(4)=\frac{1}{2}(4)+5=\frac{4}{2}+5=2+5=7[/tex]
b. [tex]g(-10)=\frac{1}{2}(-10)+5=\frac{-10}{2}+5=-5+5=0[/tex]
c. [tex]g(0)=\frac{1}{2}(0)+5=0+5=5[/tex]
Darius and Barb are playing a video game in which the higher score wins the game. Their scores are shown below.
Darius’s scores: 96, 54, 120, 87, 123
Barb’s scores: 92, 98, 96, 94, 110
Barb says that she is the winner. Darius says that it is a tie. Who is correct?
- Barb is correct if both the mean and median scores are considered.
- Barb is correct if only the median score is considered.
- Darius is correct if both the mean and median scores are considered.
- Darius is correct if only the median score is considered.
Answers
Answer:
D. Darius is correct if only the median score is considered.
Step-by-step explanation:
Answer:
The correct answer is option D: Darius is correct if only the median score is considered.
Step-by-step explanation:
I did the test and got it correct
Hope this helps! Have a nice day!
A group of friends goes out to breakfast and decides to split the bill. Their bill is $34.00, plus they want to leave an 18% tip. The final amount will be split 4 ways.
What is the amount each person will pay?
$8.50
$9.78
$10.03
$10.18
Answers
Answer:
it's 10.03
Hope this helps :D
Step-by-step explanation:
Took the test
Answer:
$10.03
Step-by-step explanation:I took the test
What is the factored form of this expression?
x2 + 9x + 16
O (X - 4)(x + 4)
O (x+4)2
O (x + 3)2
The expression cannot be factored.
Answers
Answer: The answer is D (4). The expression cannot be factored.
Please help me I would most definitely appreciate it!
Answers
So all you got to do is divide by the total by the number of people. So your answer would be 421.40/28 = $15.05
Convert to inches.
Help please
Answers
Answer:
306
Step-by-step explanation:
8.5 × 36 = 306
A camera has a listed price of $801.99 before tax. If the sales tax rate is 8.5%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
$870.16 dollars
Step-by-step explanation:
Given the following question:
Original cost = $801.99
Sales tax of 8.5%
In order to find the answer, we find 8.5% of the original cost of the camera. After that, we simply add that number to the original cost of the camera to find our answer.
[tex]\frac{8.5\times801.99}{100} =8.5\times801.99=6816.915\div100=68.16915[/tex]
[tex]68.16915[/tex]
[tex]9>5[/tex]
[tex]68.17[/tex]
Sales tax is $68.17
[tex]801.99+68.17=870.16[/tex]
Total price for the camera including tax is "$870.16."
Hope this helps.
peter comapred 2 pencils. The figure below shows the two lengths
3\4 an 5\6
what is the difference in the lengths of the 2 pencils.
Answers
Which expression is equivalent to mc014-1?
Answers
A car salesperson had $79,327 in total monthly sales in June and $88,798 in July. The salesperson earned $3,890 in commission from those combined sales.
What is the salesperson's commission as a percent of total sales for the two months?
Enter your answer, rounded to the nearest tenth of a percent, in the box.
%
Answers
Answer:
its 2.3%
Step-by-step explanation:
i did the test
Answer:
2.3%
Step-by-step explanation:
I took the test and forgot to submit my answer lol